Polynome 3, Grades mit allen Affenkästen
Author: Prof. Dr. Dörte Haftendorn

f(x)=a*x^3+b*x

Polynome 3.Grades haben zu jedem Punkt A
ihren 'Affenkasten'.

Ha 1996, 2008

Variiere b,
variiere a,
ziehe A.

Für gewünschte Extremstelle ex
ist b auf bex zu stellen.

a = 0.09 (slider from -5 to 5, step 0.01)
b = -1 (slider from -5 to 5, step 0.1)
f(x) = (a * x^(3)) + (b * x)
A = Point(f)
c = Tangent(A, f)
B, C, P = Intersect(f, c)
d = OrthogonalLine(B, xAxis)
D = Intersect(yAxis, c)
E = Midpoint(B, D)
e = OrthogonalLine(E, xAxis)
F = Intersect(f, e)
g = Tangent(F, f)
G = Intersect(d, g)
H, I = Intersect(f, g)
h = OrthogonalLine(I, xAxis)
J = Intersect(c, h)
i = OrthogonalLine(A, xAxis)
K = Midpoint(B, G)
j = Line(K, g)
poly1, b_1, j_1, i_1, g_1 = Polygon(B, J, I, G)
L = Intersect(yAxis, g)
M = Intersect(i, g)
N = Intersect(h, j_1)
O = Intersect(j, h)
l = Segment(D, L)
m = Segment(A, M)
n = Segment(K, O)
k = Segment(E, F)
Text1: "= " + f
Q, R = Extremum(f)
ex = 2
bex: ((-3 * a) * ex^(2))